Issues in Applying Financial Econometrics to Factor-Based Modeling in Investment Management

The authors summarize techniques, pitfalls, and strategies for developing, testing, and using factor models.  In defining the optimum factors to have in the model, they summarize that it is when the residuals are uncorrelated.  They then summarize the Principal Components Analysis (PCA) method for determining the number of factors.  They then explain the problems of overfitting (too many polynomial degrees) and dimentionality (too many parameters), and techniques for preventing both: for example, Regularization Theory proposes a penalty to the error for in-sample models.  The authors then go into the dangers of relying on in-sample backtesting, and they note other research that posits a 50% penalty on in-sample Sharpe ratios.

ENGLE, R. F., FOCARDI, S. M., & FABOZZI, F. J. (2016). Issues in Applying Financial Econometrics to Factor-Based Modeling in Investment Management. Journal Of Portfolio Management, 42(5), 94-106.